Conceptual Overview: Explore how the probability of the union of two events equa

Question

Conceptual Overview: Explore how the probability of the union of two events equals the probability that either event occurs. The two circles shown below represent two events, A and B. The area of each circle represents the probability of the event. With no overlap you can see that the two events (the union of A and B) written as PIA u B) is the sum of their probabilikies. The union is often descrbed as an "OR statement. The union is the probability of A occring OR B occurring OR both A and B occurring simultaneously (their intersection) ofone or the other of the Drag one of the cirdes so that the circles begin to overlap. You will see that the probability of the union decreases because some probability is included in both sets (their intersection),. You can also drag the letter for each set to change its size and thus its probabilty P(A)-0.129, P(B) = 0.067, P(A U B) = 0.195

Explanation / Answer

1. P(A) = 0.164 P(B) = 0.07

P(A U B) = P(A) + P(B)

= 0.164 + 0.07

= 0.234

which is given in option b.

2. P(A) = 0.164 P(B) = 0.07

P(A B) = P(B)/2 = 0.07/2 = 0.035

P(A U B) = P(A) + P(B) - P(A B)

= 0.164 + 0.07 - 0.035

= 0.199 which is given in option d.

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